Friday, January 17, 2020

# Hillcrest applies quadratic equation to bottle rockets

Hillcrest H.S. algebra 1 students launch bottle rockets (school newspaper)

#### Algebra 1 students at Hillcrest High School in Country Club Hills, Illinois, took to the school lawn this spring to launch bottle rockets and apply the quadratic equation in the process, The Hawk Eye reports. It’s an annual warm-weather tradition at the south-suburban school for students of math teacher Kara Bucci, says the student newspaper.

Height, 8-second bottle rocket flight

The vertical height, or altitude, of a bottle rocket can be calculated or, at least, approximated by knowing that the height plotted against time is a parabola, assuming no friction and a straight-up flight. The equation for the maximum height achieved by a bottle rocket that is launched from Earth, where friction is an actual component, is given by a formula known as Littlewood’s law, named after JE Littlewood, a mathematician in the British military during World War I.

Although this isn’t a “law” in the scientific sense, Mr Littlewood’s equation relates the altitude at apogee to the total duration of the flight, from the time the rocket is launched to the time it returns to the ground:

$h=0.122 \cdot g \cdot t^2$

where h is the altitude at apogee, t is the total duration of the flight from launch to touchdown, and g is the acceleration of gravity, which is about 9.8 m/s2.

Say the rocket stays in the air for exactly 8 seconds, as determined by a student with a stopwatch. We can calculate the approximate height at apogee as follows:

$h=(0.122 \cdot 9.8 \cdot 8^2)\textrm{ m}$
$h \approx 76.52\textrm{ m} \approx 250\textrm{ feet}$
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

### Feds boost Bay funding

Restoration efforts in the Chesapeake Bay watershed received a boost in federal funding in the budget Congress passed last month.

### Md. & IL bands perform on New Year’s in...

Bands from IL and Md. once again entertained thousands of people who lined the streets of London and Rome on New Year's Day.

### Howard Co. sounds an under-staffing alarm

Teachers in a Md. district have filed a grievance over missing planning and lunch periods and, as a result, putting the most vulnerable students at risk.

### Top 11 school stories of 2019

We find these 11 stories to have the greatest potential for influencing activity and direction in schools for the near future.

### Girls’ volleyball champs in Illinois

We congratulate the Illinois state champions in girls' volleyball: Newark, St Teresa, Sterling, & Benet Academy.

### A weekend of ‘band geeks’ across America

The musical Band Geeks was in performance at a MD high school, just as marching bands from across America named a national champion.

### 2 dead, 3 wounded in Calif. school shooting

Another school shooting has resulted in the death of 2 California high school students. The suspect shot himself and is in custody.

### Mercury makes a transit; next in 2032

A transit of Mercury occurred today and was visible from the US, provided you had sunny skies. It was one of longest possible transits.

### On the Naperville BWW racist incident

A racist incident at a Naperville, IL, sports bar indicates that the threads of racism are strong, perhaps as strong as ever.

### IL bill could excuse absences to vote

A proposed law in IL could give students up to two hours during the school day so they could vote in the upcoming election.

### Loan forgiveness gains some bipartisan support

One Republican from GA, who used to work under Betsy DeVos at the US Education Dept, offers a plan to forgive some student loan debt.